_flint_mpn_gcdext_inplace

The extended GCD with the interface of GMP's mpn_gcdext: sets $(\mathit{gp}, \ell)$ to $g = \gcd(u, v)$, returning $\ell$, and $(\mathit{sp}, |{*\mathit{sn}}|)$ with the sign of $*\mathit{sn}$ to the cofactor $s$ of $u$ as for flint_mpn_gcdext. It is required that $\mathit{un} \ge \mathit{vn} > 0$ and that the top limb of $v$ is nonzero; the top limb of $u$ may be zero, so that $u$ can be padded to the length of $v$ to obtain its cofactor directly (as for a modular inverse). Both inputs are destroyed, and both input arrays must have room for one more limb. gp needs room for $\mathit{vn}$ limbs and sp for $\mathit{vn} + 1$ limbs; they must not overlap each other or the inputs.